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Avery is designing a large rectangular sign. They want the sign to have an area of
2m^(2) and a width of
(4)/(5)m.
How tall should the sign be?
m

Avery is designing a large rectangular sign. They want the sign to have an area of $2 \mathrm{~m}^{2}$ and a width of $\frac{4}{5} \mathrm{~m}$ . $\newline$ How tall should the sign be? $\newline$ m

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Scale drawings: word problems

Full solution

Q. Avery is designing a large rectangular sign. They want the sign to have an area of

2 \mathrm{~m}^{2}

and a width of

\frac{4}{5} \mathrm{~m}

.

\newline

How tall should the sign be?

\newline

m

Area Formula: To find the height of the sign, we need to use the formula for the area of a rectangle, which is $\text{Area} = \text{Width} \times \text{Height}$ . We know the $\text{Area}$ and the $\text{Width}$ , so we can solve for the $\text{Height}$ .
Given Values: The area of the sign is given as $2$ square meters ( $2\,\text{m}^2$ ), and the width is given as $\frac{4}{5}$ meters ( $\frac{4}{5}\,\text{m}$ ). Let's denote the height as $H$ meters ( $H\,\text{m}$ ).
Area Calculation: Using the area formula, we have: $\newline$ Area = Width $\times$ Height $\newline$ $2m^2 = \left(\frac{4}{5}\right)m \times Hm$
Height Calculation: To find the height ( extit{H}), we need to divide the area by the width: $\newline$ extit{H} = extit{Area} / extit{Width} $\newline$ extit{H} = $2m^2$ / $(4/5)m$
Division and Multiplication: Now we perform the division: $\newline$ $H = \frac{2m^2}{\left(\frac{4}{5}\right)m}$ $\newline$ To divide by a fraction, we multiply by its reciprocal: $\newline$ $H = 2m^2 \times \left(\frac{5}{4}\right)$
Final Height: Multiplying the two values gives us the height: $\newline$ H = $(2 \times 5) / 4$ $\newline$ H = $10 / 4$ $\newline$ H = $2.5$ m

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